Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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15 views

Static hedge for Down-and-out put option

I am trying to compute the static hedge for a down-and-out put option with the barrier above the strike using the put-call symmetry. I am okay with the example in the note with the call option but I ...
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Open interest and price evolution - wikipedia article

The Wikipedia article on open interest ends with the following table, itself sourced from a McGraw-Hill Professional book. Seems legit, but I am surprised: I thought there was no provable relation ...
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How to model the effect of an asset with a neutral return on another asset

Disclaimer: Am a software engineer by training, diving into finance. Am still a noob xD Hey team, I have been reading one of Spitznagel's whitepapers: https://www.universa.net/...
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Hedging a short position in the Lookback Option

SOLUTION I got the correct answer using this formula $X_2(HH)=(1+r)*[X_1(H)-\Delta_1(H)*S_1(H)]+\Delta_1(H)*S_2(HH)$ $(1+0.25)[2.24-(.06667*8)]+0.06667*16=3.20$
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99 views

Calculate Third Order Greeks Options

Hope you're doing great! I'm struggling to develop the code for the Third Order Greeks. In all places I have searched, the development is missing. For example: But I don't know how to develop it, ...
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difficulty pricing options using stochastic volatility

can someone kindly explain why it was difficult to obtain an explicit formula for pricing options under stochastic volatility. Thanks alot.
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How to get all the paths of a binomial tree

I'm trying to implement a pricing method for exotic options based on binomial tree's. The problem i'm having is that i'm not being able to generate all the paths of the tree. I have the following code ...
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106 views

Should a normal distribution be used for valuing options on assets that can potentially have negative prices?

The Black-Scholes-Merton model assumes that the prices of the underlying asset at maturity are log-normally distributed. I understand that this assumes that the prices can never go below zero. ...
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146 views

Expected Delta hedging frequency as function of implied (and realized) volatility

I'm looking for a proxy (or some rule of thumb) that can create a link between the implied volatility, the realized volatility and the frequency of Delta hedging required to keep the Delta as close as ...
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Advice on learning C++ and its integration with Python/R/MATLAB for quantitative finance

For some background information, I am a PhD student in economics. Although I did not study in finance previously, I took a course on stochastic calculus and a course on asset pricing in incomplete ...
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Double Call Option

A double call option allows the holder to either exercise at time $T_{1}$ or time $T_{2}$, where $T_{2}$>$T_{1}$. With corresponding strike prices $K_{1}$ and $K_{2}$, it can be shown that it is never ...
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Maximizing a GARCH likelihood: Good practice on constraining solutions and initial values

I am currently working on option pricing model and I'd like to include a method for maximizing the likelihood of returns under the P measure. I am using the Heston and Nandi (2000) model: \begin{align}...
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Historical S&P 500 OPTION data on WRDS, no access to Option Metrics

I'm looking for historical data of S&P500 options. I have access to Wharton Research Data Services (WRDS), however, my university does not provide access to Option Metrics. Is there another way ...
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How to model/price the risk of Covid-19 and other pandemics

How would you model and price the risk of Covid-19 pandemic? These large cost low probability events with very little history seems to pose a particular challenge when quantitatively modeling and ...
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147 views

Empirical correlation between the price of a call option and the underlying stock

I am not sure if this question is appropriate here, but I am just going to give a shot. It is related to an empirical observation about the price of a call option. Specifically, I was looking at a ...
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382 views

Problem with the concept of Dollar Gamma

I was reading up on variance swaps and encounter the notion of Dollar Gamma, which is defined as the change in dollar value of the Dollar Delta (Δ * S) for a 1% change in spot (S). The formula for ...
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115 views

How to manage theta, gamma, vega, and delta risk in options market making simulation

I'm just starting to learn how to trade options and as part of an algorithmic options market making simulation I have risk limits for the greeks (gamma, vega, delta, and theta). There are 9 strikes ...
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29 views

Reference for “an increase in volatility increases value/price of american options”

I'm looking for a textbook/journal article reference for the well-known result that an increase in volatility increases the value/price of a standard American (call and put) option. In the case of ...
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40 views

Assymmetric Risk Call Option

I'm reading in Radu Tunaru's book "Model Risk in Financial Markets" and he argues that two parties in the financial contract do not have the same magnitude of exposure to model risk. The reason for ...
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99 views

how to price options in reality [closed]

I'm getting to know the Black Scholes model, which apparently is no longer suitable for pricing options on the market. I would like to write a Master's thesis on option pricing but I do not know what ...
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64 views

Most profitable PUT strike price in these times of high volatility?

At close 3/13/20 SPY was at 270.2, by close 3/16 it dropped to 239.41 ~ 8.8% drop... I'm looking at how to capitalize on these big swings with options. I'm backtesting option strategies and plotted ...
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What are some heurestics you could use to judge if skew is cheap or expensive? If any?

Are there rules of thumbs/models that you could use to develop intuition for when skew is cheap or expensive? From what I gather, volatility is a number that is backed out of price in a sense, "the ...
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Is there an options screening site that allows you to specify Bid, Ask, or Midpoint for conditions?

Is there an options screener that allows choosing the basis for conditional comparisons? e.g. Show me options where the BID implies a volatility greater than X% Show me options where the ASK implies ...
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How can I calculate returns for three investment strategy?

Assume that the price of DF stock went from a price of $104 on March 2 to 146 on April 1. With a current stock price of 146, there is a call option available on the DF stock with an exercise price ...
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Calculate 6 month- return for an investment [closed]

Assume that the price of DF stock went from a price of $104 on March 2 to 146 on April 1. With a current stock price of 146, Invest all of your amount 14,600 in the DF stock (buy 100 shares) ...
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Question about the writing a call option on an existing portfolio of stocks [closed]

My question is Please discuss about the following statement “ the advantages and disadvantages of writing a call option on an existing portfolio of stocks” Note that I read an article nearly ...
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144 views

Why are options on commodity futures traded instead of options on spot commodities?

When people mention "commodity options", they almost invariably mean "options on commodity futures contracts". Why do commodity options have futures as underlying, and not the commodities themselves ...
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CVA for a portfolio of long and short options

I am looking to estimate the CVA/DVA for a portfolio of options. For simplicity sake, let's assume there are two FX options in the portfolio, one long and one short. Both options have the same ...
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Intuition behind prices modeled by Geometric Brownian Motion

Suppose that we model a price $P_t$ to evolve per $$\frac{dP_t}{P_t}=\mu dt+\sigma dW_t$$ for $\mu\in\mathbb{R}$ and $\sigma>0$. The unique strong solution to this diffusion is $$P_t=P_0e^{(\mu-\...
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Question about financial mathematics, meeting a claim

I have a question regarding exercise 12, chapter 1 of "A course in Financial Calculus" by Alison Etheridge. It is as follows: "Suppose that the value of a certain stock at time $T$ is a random ...
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Create a Synthetic Single Stock Future

Is it possible to create a synthetic long single stock future using the stock and it's vanilla options with the caveat that selling naked puts is NOT allowed? That is, you can write puts, but they ...
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209 views

Why do some principal-protected notes reset the gains to zero?

I was looking through the principal-protected notes issued by Lehman Brothers. One of them was the "100% Principal Protection Absolute Return Barrier Notes Linked to the S&P 500 Index". The ...
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Trading options - real life vs. textbook?

I'm a Management with Finance student and we have recently learned about options. Because I find it easier to learn these things when I have some context to apply them to, I put $100 in my brokerage ...
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63 views

Are there values of the strike price for which an American put and European put have the same no-arbitrage price?

Assuming the options do not pay dividends, is there a strike price that satisfies this?
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Is there a reason why futures and options have more substitutes than other financial instruments?

This is somewhat non-technical question, but it seems like this forum is still the best place for it. I'm reading Shleifer's Inefficient Markets, where he points out that [...] for futures and ...
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146 views

Books on options trading with a practical bent?

just curious to see if anyone here has come across a book or books on options trading with the practitioner in mind? My lecture slides for instance, go through black scholes and the ins and outs of ...
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81 views

How to price complex corporate actions with spinoffs

Let's look at below UTX/RTN merger as an example: https://www.fool.com/investing/2020/03/30/raytheon-united-technologies-merger-gets-green-lig.aspx The merged companies will from that moment ...
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96 views

Does the Black-Scholes formula work when unit of time is in hours?

In the Black-Scholes formula, the unit of time is usually in years from what I understand. An online calculator I found allows the users to input the time in days and years. Would the formula still ...
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Pricing with estimated parameters

I used daily log-returns to estimate the parameters in the Bates model, and I want to price a contingent claim using these estimates. I know that I have to distinguish between parameters estimated ...
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86 views

Black-Scholes Delta value at maturity?

Having to implement a replication strategy for European options, I encounter the following problem: Delta tells me how many shares to hold at time t in my replication strategy. To do so, I simply ...
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Average daily move from implied volatility of risk reversal

I'm trying to understand an example in Euan Sinclair's Option Trading book. On page 239 he gives a risk slide and pnl from a long 30 delta put short 30 delta call position. He says the implied ...
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73 views

Implied volatility and greeks of options

When we are calculating deltas or vegas for different strikes should we use the underlying asset's volatility or should we use the implied volatility for the specific strikes at a fixed maturity? ...
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274 views

Are there any books/articles on how to use options to be long volatility (implied or realized)? [duplicate]

Given the market turmoil of late I have become fixated with this idea of using options to be long volatility (realised and implied). However, I dont know where to start, what to read, who to follow ...
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Option Prices Affecting Underlying value Through market makers max pain

In function of the quarantine I started to dig a little deeper into the "Max Pain" principle and how market makers who write the options have to hedge the risk. What I understood so far: Options are ...
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118 views

Connecting the dots: Black Scholes, Volatility and Implied Volatility

I am a first year Management & Finance undergrad preparing for my second year Finance courses, given that term 3 and exams have pretty much been cancelled for all British first years. During that ...
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106 views

Pricing an interest rate floor

I am trying to estimate the value of a 0% interest rate floor by pricing each individual floorlet. Since BS won't work for this problem, I am trying to use normal volatility in a Bachelier model like ...
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310 views

Pricing In Real Life vs Theory

When selling/buying vanilla call options, do one price them according to some pricing formula (i.e Black-Scholes)? Or is the only point using pricing formulas to find the implied volatility and then ...
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115 views

What is the delta of an at-the-money European call option with respect to volatility?

Question: What is the delta of an at-the-money European call option with respect to volatility? Note that $$\frac{\partial\Delta}{\partial\sigma} = N'(d_1) \frac{\partial d_1}{\partial\sigma} = N'(...
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78 views

Why is there a theoretical lower bound on the price of call options?

From my textbook, I see that the theoretical lower bound for the price of a European call option on a non-dividend-paying stock is: $S_0 - \mathrm{Ke}^\mathrm{-rT}$, where $S_0$ is the current stock ...
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88 views

Is it possible to construct a hedge that matches value Delta Gamma and Vega?

Given a strike price, current price, risk free rate, dividend yield and volatility, I have been asked to calculate: - a hedge which matches the value Delta and Gamma - a hedge which matches the value ...

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